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Chapter1_9

# Chapter1_9 - frames of reference i.e same in O and O frame...

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PHY3063 R. D. Field Department of Physics Chapter1_9.doc University of Florida 4-Vector Notation 4-vector “dot product”: Define the 4-vector dot product as follows: 2 3 2 2 2 1 2 0 2 0 ~ ~ x x x x r r x r r = r r where = 3 2 1 0 ~ x x x x r a n d = 3 2 1 x x x r r Space-Time 4-vectors: = z y x ct r ~ = z y x t c r ~ = 1 0 0 0 0 1 0 0 0 0 0 0 γ βγ L = 1 0 0 0 0 1 0 0 0 0 0 0 1 L 2 1 / 1 / β = = c V Lorentz Transformations: r L r = ~ ~ r L r ~ ~ 1 = Lorentz Invariant: A “Lorentz invariant” is any quantity that is the same in all inertial
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Unformatted text preview: frames of reference ( i.e. same in O and O' frame). The square of a Lorentz 4-vector is a Lorentz invariant ( i.e. Lorentz scalar ). 2 2 ) ~ ( ~ ~ ~ ~ ~ r r r r r r ′ = ′ ⋅ ′ = ⋅ = Any four quantities that transform from O' to O according to Lorentz forms a Lorentz 4-vector Same in all inertial frames of reference 4-vector 3-vector 3-vector dot product...
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